Energy funneling effect and charge transfer behavior of MoS<sub>2</sub> with thickness gradient

ZUO Huiling; SHEN Quan; LI Jing; LIU Jing; DONG Jiansheng

doi:10.7498/aps.74.20250661

Abstract

Energy funneling effect of two-dimensional materials provides an important method for modulating carrier transfer. However, the formation of energy funneling and its influences on the carrier transfer are still relatively uncharacterized. In this work, the energy funneling induced by the layer number gradient effect in MoS₂ is investigated through atomic-bond-relaxation approach and first-principles calculations. It is found that the bandgap of MoS₂ monotonically increases with the decrease of the layer number, leading the conduction band minimum (valence band maximum) of thin layer MoS₂ to be higher than (lower than) that of thick layer MoS₂. Therefore, both dual thickness gradient and triple thickness gradient MoS₂ can achieve the energy funneling effect. As a result, the carriers will be directionally transferred from the thin layer region to the thick layer region. According to Marcus theory, the carrier transfer rate is dependent on drive force caused by the energy level difference with different thicknesses of MoS₂. For the dual thickness gradient MoS₂, when the thickness difference between adjacent layers is the largest, the driving force is the highest, which is 1L/bulk. In addition, owing to the driving force smaller than the reorganization energy in dual thickness gradient MoS₂, a large driving force corresponds to a high carrier transfer rate, resulting in a higher carrier transfer rate of 1L/bulk than those in other dual thickness gradient systems. For the triple thickness gradient MoS₂, there are two consecutive interface energy differences that induce driving forces. However, the carrier transfer rate is exponentially correlated with the driving force. Therefore, the carrier transfer rate of dual thickness gradient MoS₂ will be higher than that of the corresponding triple thickness gradient MoS₂. Our results demonstrate that the energy funneling effect induced by thickness gradient can realize carrier accumulation in the thick layer region without the need for p-n junctions, which is of great benefit in collecting photogenerated carriers. The atomic force microscopy lithography and chemical vapor deposition will be used to engineer thickness-gradient two-dimensional materials with enhanced optoelectronic properties in future.

Keywords:

Authors and contacts

College of Physics and Electromechanical Engineering, Jishou University, Jishou 416000, China

Corresponding author: DONG Jiansheng, jsdong@jsu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12364007), the Basic Research Program for Young Students of Natural Science Foundation of Hunan Province, China (Grant No. 2025JJ60929), the Scientific Research Foundation of Hunan Provincial Education Department, China (Grant No. 24A0366), and the Hunan Students’ Platform for Innovation and Entrepreneurship Training Program, China (Grant No. S202310531036).

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References

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Cited By

图 1 (a) 双厚度梯度MoS₂结构示意图; (b) 双厚度梯度MoS₂能带漏斗及其对电荷转移示意图; (c) 三厚度梯度MoS₂结构示意图; (d) 三厚度梯度MoS₂能带漏斗及其对电荷转移示意图

Figure 1. (a) Schematic diagrams of dual thickness gradient MoS₂; (b) energy funneling and its effect on carrier transfer in dual thickness gradient MoS₂; (c) schematic diagrams of triple thickness gradient MoS₂; (d) energy funneling and its effect on carrier transfer in triple thickness gradient MoS₂.

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图 2 (a) 不同层数MoS₂势函数与原子间距之间的关系; (b) MoS₂层数依赖的带隙漂移, 插图是MoS₂导带底和价带顶随层数的变化规律

Figure 2. (a) Relationship between potential and distance of MoS₂ with different layer number; (b) layer number dependent bandgap of MoS₂, the inset of (b) shows the conduction band minimum (CBM) and valence band maximum (VBM) of MoS₂ as a function of layer number.

DownLoad: Full-Size Img PowerPoint

图 3 不同层数MoS₂的能带结构

Figure 3. Band structures of MoS₂ with different layer.

DownLoad: Full-Size Img PowerPoint

图 4 (a) 双厚度梯度MoS₂界面能级差诱导的驱动力; (b) 双厚度梯度MoS₂中的能带漏斗对电荷转移速率影响; (c) 三厚度梯度MoS₂界面能级差诱导的驱动力; (d) 三厚度梯度MoS2中的能带漏斗对电荷转移速率影响

Figure 4. (a) Driving force induced by the energy level difference in dual thickness gradient MoS₂; (b) the effect of energy funneling on the charge transfer rate in dual thickness gradient MoS₂; (c) the driving force induced by the energy level difference in triple thickness gradient MoS₂; (d) the effect of energy funneling on the charge transfer rate in triple thickness gradient MoS₂.

DownLoad: Full-Size Img PowerPoint

[1]	Jiang H, Zhang X K, Chen K L, He X Y, Liu Y H, Yu H H, Gao L, Hong M Y, Wang Y, Zhang Z, Zhang Y 2025 Nat. Mater. 24 188 Google Scholar
[2]	Zhao J J, Liao M Z, Shen C, Wang Q Q, Yang R, Watanabe K, Taniguchi T, Huang Z H, Shi D X, Liu K H, Sun Z P, Feng J, Du L J, Zhang G Y 2025 Phys. Rev. Lett. 134 086201 Google Scholar
[3]	Mak K F, Lee C, Hone J, Shan J, Heinz T F 2010 Phys. Rev. Lett. 105 136805 Google Scholar
[4]	Li L K, Yu Y J, Ye G J, Ge Q Q, Ou X D, Wu H, Feng D L, Chen X H, Zhang Y B 2014 Nat. Nanotechnol. 9 372 Google Scholar
[5]	邓文, 汪礼胜, 刘嘉宁, 余雪玲, 陈凤翔 2021 物理学报 70 217302 Google Scholar Deng W, Wang L S, Liu J N, Yu X L, Chen F X 2021 Acta Phys. Sin. 70 217302 Google Scholar
[6]	Yang F, Hu Y T, Ou J L, Li Q Y, Xie X X, Han H P, Cai C L, Ruan S C, Xiang B X 2025 ACS Photonics 12 2128 Google Scholar
[7]	Feng J, Qian X F, Huang C W, Li J 2012 Nat. Photonics 6 866 Google Scholar
[8]	Li H, Contryman A W, Qian X F, Ardakani S M, Gong Y J, Wang X L, Weisse J M, Lee C H, Zhao J H, Ajayan P M, Li J, Manoharan H C, Zheng X L 2015 Nat. Commun. 6 7381 Google Scholar
[9]	Harats M G, Kirchhof J N, Qiao M X, Greben K, Bolotin K I 2020 Nat. Photonics 14 324 Google Scholar
[10]	Lee J, Yun S J, Seo C, Cho K, Kim T S, An G H, Kang K, Lee H S, Kim J 2021 Nano Lett. 21 43 Google Scholar
[11]	刘俊杰, 左慧玲, 谭鑫, 董健生 2024 物理学报 73 236801 Google Scholar Liu J J, Zuo H L, Tan X, Dong J S 2024 Acta Phys. Sin. 73 236801 Google Scholar
[12]	Sun Z Y, Li Y, Xu B, Chen H, Wang P, Zhao S X, Li Y, Gao B, Dou X M, Sun B Q, Zhen L, Xu C Y 2021 Adv. Opt. Mater. 9 2100438 Google Scholar
[13]	Xu N, Pei X D, Qiu L P, Zhan L, Wang P, Shi Y, Li S L 2023 Adv. Mater. 35 2300618 Google Scholar
[14]	Ouyang G, Wang C X, Yang G W 2009 Chem. Rev. 109 4221 Google Scholar
[15]	Zhu Z M, Zhang A, Ouyang G, Yang G W 2011 Appl. Phys. Lett. 98 263112 Google Scholar
[16]	Dong J S, Zhao Y P, Ouyang G, Yang G W 2022 Appl. Phys. Lett. 120 080501 Google Scholar
[17]	Sun C Q 2007 Prog. Solid State Chem. 35 1 Google Scholar
[18]	Jiang J W, Park H S, Rabczuk T 2013 J. Appl. Phys. 114 064307 Google Scholar
[19]	Xiong S, Cao G X 2015 Nanotechnology 26 185705 Google Scholar
[20]	Zhu Y F, Jiang Q 2016 Coordin. Chem. Rev. 326 1 Google Scholar
[21]	Marcus R A 1956 J. Chem. Phys. 24 966 Google Scholar
[22]	Zhang C, Lian L Y, Yang Z L, Zhang J B, Zhu H M 2019 J. Phys. Chem. Lett. 10 7665 Google Scholar
[23]	Kresse G, Hafner J. 1993 Phys. Rev. B 47 558 Google Scholar
[24]	Blöchl P E 1994 Phys. Rev. B 50 17953 Google Scholar
[25]	Kresse G 1996 Phys. Rev. B 54 11169 Google Scholar
[26]	Yun W S, Han S W, Hong S C, Kim I G, Lee J D 2012 Phys. Rev. B 85 033305 Google Scholar
[27]	Li T S 2012 Phys. Rev. B 85 235407 Google Scholar
[28]	Kang J, Tongay S, Zhou J, Li J B, Wu J Q 2013 Appl. Phys. Lett. 102 012111 Google Scholar
[29]	Dong J S, Liu J J, Liao W H, Yang X X, He Y, Ouyang G 2024 J. Appl. Phys. 136 125302 Google Scholar
[30]	Chu T, Ilatikhameneh H, Klimeck G, Rahman R, Chen Z H 2015 Nano Lett. 15 8000 Google Scholar
[31]	Lee H S, Min S W, Chang Y G, Park M K, Nam T, Kim H, Kim J H, Ryu S, Im S 2012 Nano Lett. 12 3695 Google Scholar
[32]	Wang J H, Ding T, Gao K M, Wang L F, Zhou P W, Wu K F 2021 Nat. Commun. 12 6333 Google Scholar
[33]	Furchi M M, Pospischil A, Libisch F, Burgdörfer J, Mueller T 2014 Nano Lett. 14 4785 Google Scholar
[34]	Lee C H, Lee G H, Zande A M, Chen W C, Li Y L, Han M Y, Cui X, Arefe G, Nuckolls C, Heinz T F, Guo J, Hone J, Kim P 2014 Nat. Nanotechnol. 9 676 Google Scholar
[35]	Cao G Y, Shang A X, Zhang C, Gong Y P, Li S J, Bao Q L, Li X F 2016 Nano Energy 30 260 Google Scholar

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Energy funneling effect and charge transfer behavior of MoS₂ with thickness gradient

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Corresponding author: DONG Jiansheng, jsdong@jsu.edu.cn

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Energy funneling effect and charge transfer behavior of MoS2 with thickness gradient

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Corresponding author: DONG Jiansheng, jsdong@jsu.edu.cn

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Energy funneling effect and charge transfer behavior of MoS₂ with thickness gradient